Math 101 -- Practice Problems
Carry out the operations indicated and simplify if possible.
1. 2 + 3(5 ! 1)
2. 8! ("4) + 3 ! (4 " 6)
3. 2(3 ! 1) ! 3( 2 ! 5)
4. (!2)(!3) ! (!4)(!5)
5.
!2 " 3 %
!$ '
3 # !4 &
1
1
1
6. 7 + 14 + 21
3
2
7. 25 + 35
8.
3!5 5!3
"
2 !5 2!3
4
9
9. 9 ÷ 4
In problems 9 - 12, solve the given equation for x.
10. 3(x ! 1) + 2(x + 1) = 9
11. 4( 2x ! 1) ! 3(x + 1) = 8
12.
x + 2 x +1
=
5
3
-213. 1.301 - .211 + .0004 = ?
14. 9.603 ÷ .003 = ?
15. 13 is what % of 52?
16. What is 1% of .01?
17. A certain city charges 7% meal tax in its restaruants. In that city, what is the meal tax on a
dinner priced at $40?
18. A rectangle has perimeter 18 in. If the rectangle is 3 in. wider than it is high, what is its
area?
19. What is the slope of the line throught the points (2, 3) and (1, -1) ?
20. What is the equation of the line with slope 3 which goes through the point (-2, 1) ?
21. Sketch the line whose equation is: y = 1 - x.
22. Solve the equations:
x+y=4
2x + 3y = 6
23. Solve the equations:
2x + 3y = 1
3x - 2y = -5
24. Part of $9000 is invested at 6% per year, and the rest is invested at 7% per year.
If the total interest after the first year is $610, how much was invested at each rate?
25. Todd and Terri are 3 years apart in age. 15 years ago, Terri was 4 times as old as Todd was.
How old are they both now?
-326. I’m thinking of two numbers. Their sum is 19 and their difference is 3.
Find the two numbers.
In problems 27 - 32, carry out the operations indicted and simplify if possible.
27, x 3 y ! (2x 2 y 2 + 5x 2 y 2 )
x 3y 2z 3
28.
2
( xyz)
29.
x x
+
2 3
30.
4x 3 y 4 + 2x 2 y 5 ! 6x 3 y 3
2x 2 y 2
31.
x 3 + 3x 2 + 5x + 6
x+2
32.
x3 ! x + 2
x!1
In problems 33 - 38, factor the given expression as completely as possible.
4
2
33. x + 3x
2
34. 3x ! 300
3
2
35. 3x + 6x + 3x
2
36. x ! 4x ! 21
2
37. x ! 11x + 24
2
38. x + 12x + 35
In problems 39 - 43, solve the given equation for x.
2
39. x ! 25 = 0
-4-
2
40. x = 56 + x
41. 2( x + 2) ! ( x + 1) = 14
2
2
2
42. x + 1 = 3 ! x
43.
x 2 + 3x ! 4
=0
x 2 ! 2x + 1
44. The area of a certain rectangle is 40 sq. in. If the rectangle is 3 in. longer than it is wide,
what is its perimeter?
45. The sum of two numbers is 5, and their product is -36. Find the numbers.
46. Solve for x:
x3 ! x x2 ! x
.
=
2
3
47. Solve for x:
2x + 3x + 1 = 0 .
2
48. The difference of two numbers is 9. Their product is 52. Find the numbers.
2
49. Solve for x: x ! 2x ! 4
2
50. Solve for x: x + x ! 100